# Population process

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In [applied probability](/source/applied_probability), a '''population process''' is a [Markov chain](/source/Markov_chain) in which the state of the chain is analogous to the number of individuals in a population (0, 1, 2, etc.), and changes to the state are analogous to the addition or removal of individuals from the population. Typical population processes include [birth–death process](/source/birth%E2%80%93death_process)es and [birth, death and catastrophe process](/source/birth%2C_death_and_catastrophe_process)es.<ref name="transact">{{cite book |editor1-last=Priami |editor1-first=Corrado |editor2-last=de Vink |editor2-first=Erik |editor3-last=Petre |editor3-first=Ion |title=Transactions on Computational Systems Biology XIV |date=28 November 2012 |publisher=Springer Berlin Heidelberg |isbn=9783642355240 |pages=4–5 |url=https://books.google.com/books?id=7lO5BQAAQBAJ |access-date=17 April 2023}}</ref>

Although named by analogy to [biological](/source/biology) populations from [population dynamics](/source/population_dynamics), population processes find application in a much wider range of fields than just [ecology](/source/ecology) and other biological sciences.  These other applications include [telecommunications](/source/telecommunications) and [queueing theory](/source/queueing_theory), [chemical kinetics](/source/chemical_kinetics) and [financial mathematics](/source/financial_mathematics), and hence the ''population'' could be of [packet](/source/packet_switching)s in a [computer network](/source/computer_network), of [molecule](/source/molecule)s in a [chemical reaction](/source/chemical_reaction), or even of units in a [financial index](/source/stock_market_index).  

Population processes are typically characterized by processes of birth and immigration, and of death, emigration and catastrophe, which correspond to the basic [demographic](/source/demography) processes and broad [environment](/source/natural_environment)al effects to which a population is subject.  However, population processes are also often equivalent to other processes that may typically be characterized under other [paradigm](/source/paradigm)s (in the literal sense of "patterns").  [Queues](/source/queueing_theory), for example, are often characterized by an arrivals process, a service process, and the number of servers.  In appropriate circumstances, however, arrivals at a queue are functionally equivalent to births or immigration and the service of waiting "customers" is equivalent to death or emigration.  

==See also==
* [Moran process](/source/Moran_process)

==References==
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Category:Population
Category:Markov models

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Adapted from the Wikipedia article [Population process](https://en.wikipedia.org/wiki/Population_process) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Population_process?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.